Buzzard: Difference between revisions

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Created page with "{{Infobox regtemp | Title = Buzzard | Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.11.13 | Comma basis = 65536/64827 (2.3.7); <br>1728/1715, 5120/5103 (7-limit);<br>176/175, 351/350, 540/539, 676/675<br>(13-limit) | Edo join 1 = 53 | Edo join 2 = 58 | Mapping = 1; 4 21 -3 39 27 | Generators = 21/16 | Generators tuning = 475.7 | Optimization method = CWE | MOS scales = 3L 2s | Ploidacot = alpha-tetracot | Pergen = | Color name = | Odd limit 1 = 2.3.7..."
 
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| Odd limit 2 = 15 | Mistuning 2 = 4.09 | Complexity 2 = 43
| Odd limit 2 = 15 | Mistuning 2 = 4.09 | Complexity 2 = 43
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'''Buzzard''' is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the simplest non-[[Slendric]] 2.3.7 temperament since it equates two 64/63's with one 49/48. Since Buzzard sharpens 147/128, it can be extended to 2.3.7.13/5 by tempering out the huntsma, 640/637.
'''Buzzard''', {{e|48}} & {{e|53}}, is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after [[Slendric]]" since it equates two (not one) 64/63's with one 49/48, exaggerating the difference between 21/16 and 64/49. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.
 
== List of patent vals ==
{| class="wikitable"
|+
!Edo
!Fifth tuning
!7/4 tuning
!Generator tuning
|-
|23
|678.26
|991.30
|469.57
|-
|28
|685.71
|985.71
|471.43
|-
|33
|690.91
|981.82
|472.73
|-
|38
|694.74
|978.95
|473.68
|-
|43
|697.67
|976.74
|474.42
|-
|48
|700.00
|975.00
|475.00
|-
|101
|700.99
|974.26
|475.25
|-
|53
|701.89
|973.58
|475.47
|-
|111
|702.70
|972.97
|475.68
|-
|58
|703.45
|972.41
|475.86
|-
|179
|703.91
|972.07
|475.98
|-
|121
|704.13
|971.90
|476.03
|-
|184
|704.35
|971.74
|476.09
|-
|63
|704.76
|971.43
|476.19
|-
|131
|705.34
|970.99
|476.34
|-
|68
|705.88
|970.59
|476.47
|-
|73
|706.85
|969.86
|476.71
|-
|78
|707.69
|969.23
|476.92
|-
|83
|708.43
|968.67
|477.11
|-
|5
|720.00
|960.00
|480.00
|}
 
{{Navbox regtemp}}
{{Cat| temperaments}}

Latest revision as of 14:20, 14 April 2026

Buzzard
Subgroups 2.3.7, 2.3.5.7, 2.3.5.7.11.13
Reduced mapping ⟨1; 4 21 -3 39 27]
ET join 53 & 58
Generators (CWE) ~21/16 = 475.7¢
MOS scales 3L 2s
Ploidacot alpha-tetracot
Comma basis 65536/64827 (2.3.7);
1728/1715, 5120/5103 (7-limit);
176/175, 351/350, 540/539, 676/675
(13-limit)
Minimax error 2.3.7 9-odd-limit: 3.42¢;
15-odd-limit: 4.09¢
Target scale size 2.3.7 9-odd-limit: 13 notes;
15-odd-limit: 43 notes

Buzzard, ​48 & ​53, is a 2.3.7 temperament that splits 3/1 into four sharpened 21/16 subfourths. It can be considered the "simplest 2.3.7 temperament after Slendric" since it equates two (not one) 64/63's with one 49/48, exaggerating the difference between 21/16 and 64/49. Since Buzzard sharpens 147/128, equating it to an exact semifourth at -2 generators, it can be extended to 2.3.7.13/5 by equating 147/128 to 15/13, thus tempering out the huntsma, 640/637.

List of patent vals

Edo Fifth tuning 7/4 tuning Generator tuning
23 678.26 991.30 469.57
28 685.71 985.71 471.43
33 690.91 981.82 472.73
38 694.74 978.95 473.68
43 697.67 976.74 474.42
48 700.00 975.00 475.00
101 700.99 974.26 475.25
53 701.89 973.58 475.47
111 702.70 972.97 475.68
58 703.45 972.41 475.86
179 703.91 972.07 475.98
121 704.13 971.90 476.03
184 704.35 971.74 476.09
63 704.76 971.43 476.19
131 705.34 970.99 476.34
68 705.88 970.59 476.47
73 706.85 969.86 476.71
78 707.69 969.23 476.92
83 708.43 968.67 477.11
5 720.00 960.00 480.00


View • Talk • EditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot Meantone • Schismic • Gentle-fifth temperaments • Archy
Complexity 2 Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot)
Complexity 3 Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot)
Complexity 4 Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot)
Complexity 5-6 Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot)
Higher complexity Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot)
Straddle-3 A-Team (alter-tricot) • Machine (alter-monocot)
No-3 Mabilic (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperaments Dicot • Mavila • Father
Higher-rank
Rank-3 Hemifamity • Marvel • Parapyth
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